## 7.4. Lebesgue Integral

### Definition 7.4.16: Lebesgue Integral of Non-Negative Functions

If

*f*is a non-negative measurable function defined on*and***E***h*is a bounded measurable function such that*m( {x: h(x) # 0} )*is finite, then we defineIf_{E}f(x) dx = sup{_{E}h(x) dx, h f }

*is finite, then*_{E}f(x) dx*f*is called Lebesgue integrable over*.***E**